In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such that AE : ED=2: 1. Given that OA = a, OB = b and OC = c, express OD and OE in terms of a, b and c.
Answers
Answer:
Step-by-step explanation:
CB=OB-OC;
CD=CB/2=(OB-OC)/2=(b-c)/2;
OD=OC+CD=c+(b-c)/2=c/2+b/2;
AD=OD-OA=c/2+b/2-a;
AE=2/3*AD=2/3*(c/2+b/2-a)=c/3+b/3-2*a/3;
OE=OA+AE=a+c/3+b/3-2*a/3=a/3+b/3+c/3;
-------------------------------------------------------------------------------------------------
OD=c/2+b/2;
OE=a/3+b/3+c/3;
The value of OE = (a+ b+ c)/3 and OD = (b + c)/2.
In quadrilateral OABC, we are given that D is the midpoint of BC,
and E is a point on AD such that AE : ED = 2 : 1.
Also, OA = a, OB = b and OC = c
Now, By the Midpoint Theorem, we also have
OD = (1/2)OB + (1/2)OC.
OD = (1/2)(OB + OC)
OD = (1/2)(b + c)
OD = (b + c)/2.
and, CD= (OB- OC)/2 = (b-c)/2
Now, AD=OD-OA= (c+b)/2 - a
and, AE=2/3 x AD
= 2/3 x (c+ b)/2 - a
= (c + b - 2a)/3
Then, OE = OA + AE
= a + (c + b - 2a)/3
= (a+ b+ c)/3
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Related Questions
Shoes sold at the Shoe Express are discounted 25% off the original price. If a pair of shoes originally cost $46, calculate the sale price of the shoes
Answers
Answer:
$34.50
Step-by-step explanation:
$46*.25 = $11.50
$46 - 11.50 = $34.50
Solution:
We know that:
Discounted price: Original price - (Original price × Discount)Original cost of a pair of shoes: $46Discount: 25%This means that:
Sale price of a pair of shoes: 46 - (46 × 25%)Step-1: Convert "25%" into a fraction.
25% = 25/100 = 1/4Step-2: Find the discounted price.
Sale price of a pair of shoes: 46 - (46 × 1/4)Sale price of a pair of shoes: 46 - (23/2)Sale price of a pair of shoes: 46 - 11.5Sale price of a pair of shoes: $34.5Find the value of x, y and z.
Answers
Answer:
Step-by-step explanation:
Can you help with this question I will give you 10 points
Answers
Answer:
The elevation of University Peak could be 14,464, which in between the two mountains.
Answer:
It's shorter than Mt. Massive but it's shorter than Mt. Alverstone.
The number between 14,500 and 14,428 is 14464, that would be a great guess
The function H
gives the height, above the ground, of a point on a spinning wheel. The function A gives the height of a point on a different spinning wheel and is defined by
A(t)=1.2H(3t). Here, t is time in seconds since the wheels started moving. How does the spinning wheel modeled by function A compare to the wheel for H
? Explain how you know.
Answers
The expression [tex]A(t) = 1.2\cdot H(3t)[/tex] multiplies the amplitude of [tex]H(3t)[/tex] by 1.2.
Functional analysis for the model of the height of the wheel
The model of the height is represented by the following sinusoidal model:
[tex]H(3t) = D \cdot \sin [B(3t)+E][/tex] (1)
Where:
[tex]D[/tex] - Amplitude[tex]B[/tex] - Angular frequency[tex]E[/tex] - Phase angleThen, the expression [tex]A(t) = 1.2\cdot H(3t)[/tex] multiplies the amplitude of [tex]H(3t)[/tex] by 1.2. [tex]\blacksquare[/tex]
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If Jose earned 145.60 for 7 hours, how many hours would he have to work to earn $83.20?
Answers
Answer:
4 hours
Step-by-step explanation:
Each hour: 145.60/7 = 20.80
83.20/20.80 = 4
What is the height of the trapezoid?
Answers
Answer:
don't know just wanted my points you stole
Step-by-step explanation:
6. One game system costs $238. How much will 4 game systems cost?
Answers
Answer:
Solution,
1 game cost $238
4 game cost = $238×4
= $952
I think it will help you.
Answer:
$952
Step-by-step explanation:
238×4
952
therefore 4 game system will cost $952.
RJ has two loans. Loan H has a nominal rate of 5.68%, compounded daily. Loan I has a nominal rate of 6.33%, compounded monthly. Which loan's effective rate had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan?
a.
Loan I’s increase was 0.03 percentage points greater than Loan H’s.
b.
Loan I’s increase was 0.68 percentage points greater than Loan H’s.
c.
Loan H’s increase was 0.16 percentage points greater than Loan I’s.
d.
Loan H’s increase was 0.49 percentage points greater than Loan I’s.
Answers
Answer:
The correct answer for this question is:
The loan's effective rate that had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan is that 'loan H’s increase was 0.16 percentage points greater than Loan I’s.
Step-by-step explanation:
Answer:
A: Loan I’s increase was 0.03 percentage points greater than Loan H’s.
Type the correct answer in each box.
Complete the statement, and find the value of xin the diagram.
The quadrilateral shown is a
X=
Answers
Answer:
Kite[tex]x=3[/tex]I hope this helps you
:)
Find the value of x.
Answers
Answer:
These x-values are known as the “roots” or “zeros” of the quadratic. To find these roots, we simply set the quadratic equal to zero and solve for x
Step-by-step explanation:
Help will be much appreciated...
Answers
Answer:
conclusion statement four sentences about you and exothermic heat was realised or absorbed it was changed beacsue positive 9r negative.
a box of cookies weighing 4kg was divided into 6 equal shares.
Answers
Answer:
0.67
Step-by-step explanation:
that is 4 divided by 6
your answer is 0.6666666
it's a recurring decimal
or 0.67
(-1, 2) is a solution to the following system:
equation image indicator
True
False
Answers
When x=5, the value of the expression 20/-25+x-2(x-10)is
Answers
21% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answers
Answer:
[tex]\left(a\right)\ 21.066\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(b\right)\ 66.872\\ \left(c\right)\ 81.567[/tex]
Step-by-step explanation:
[tex]\left(a\right)\ P\left(2\right)=C^{\begin{matrix}2\\10\\\end{matrix}}\bullet(32)^2\bullet(1-32)^{10-2}\\ =C^{\begin{matrix}2\\10\\\end{matrix}}\bullet(32)^2\bullet(68)^8=0.21066=21.066[/tex] [tex]percent[/tex]
[tex]cb)\ P(x > 2)=P(x\le2)=1-(P(x=0)+P(x=1)+P(x=2))\\ =1-C^{\begin{matrix}0\\10\\\end{matrix}}(0.32)degrees(0.68)^{10}-C^{\begin{matrix}1\\10\\\end{matrix}}(0.32)\prime(0.68)^9-C^{\begin{matrix}1\\0\\\end{matrix}}(008)(66)^9\\ =1-0.02114-0.09948-0.21066\\ =0.66872=66.872\\[/tex]
[tex](C)\ \ \ \ \ P(2\preccurlyeq[/tex] [tex]5)=P(2)+P(3)+P(4)+P(5)5)=P(2)+P(3)+P(4)+P(5)[/tex]
[tex]=C^{\begin{matrix}2\\10\\\end{matrix}}(0.32)^{)^2}\bullet(0.68)^3+C^{\begin{matrix}3\\10\\\end{matrix}}(0.32)^3\bullet(0.68)^7+C^{\begin{matrix}4\\10\\\end{matrix}}(0.32)^4\bullet(0.68)^6+C^{\begin{matrix}5\\10\\\end{matrix}}\bullet(0.32)^5\bullet(0.65)^5)[/tex]
[tex]=0.2186+0.26436+0.21771+0.12294\\ =0.81567=81.567 percent[/tex]
[tex](binomial\ distribution)[/tex]
I hope this helps you
:)
If we divide the polynomial P by the factor x - c and we
obtain the equation P(x) = (x – c)Q(x) + R(x), then we say
that x - c is the divisor, Q(x) is the
and R(x) is
the
Answers
Hello
Step-by-step explanation:
hello I'm Filipino people
Question 7 of 10
What is the solution to this equation?
3(4x+3) = 2x - 5(3 - x) + 2
4
O A. x=-
15
10
O B. x=-22
O
5
O x-
O c. x - 22
15
O x
O D. x = -1
5
Answers
Answer:
Option BStep-by-step explanation:
Given Equation :
[tex] \qquad \sf \dashrightarrow \: 3(4x+3) = 2x - 5(3 - x) + 2[/tex]
Using distribute property:
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 2x - 15 + 5x + 2[/tex]
Adding the like terms we get :
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 2x + 5x - 15 + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 7x - 13[/tex]
Transposing the variables on the right side and constant terms on the left side :
[tex]\qquad \sf \dashrightarrow \: 12x - 7x = - 13 - 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 5x = - 22[/tex]
Dividing both sides by 5 :
[tex]\qquad \sf \dashrightarrow \: \dfrac{5x}{5} = \dfrac{ - 22}{5} [/tex]
[tex]\qquad \bf \dashrightarrow \: x = \dfrac{ - 22}{5} [/tex]
Susan has $65 in her savings account. Her friend coco has &119 in her savings account. Susan plans to add $23 per week. How many weeks until both friends have the same amount saved ?
Answers
Answer:
After 10 weeks, Susan will have $295 and CiCi will have $259.
Step-by-step explanation:
Susan: y= 65+23x
CiCi: y = 119+14x
65+23(6)=203
119+14(6)=203
After 6 weeks, Susan and CiCi will both have $203 in their accounts.
65+23(10)=295
119+(14)(10)=259
Therefore, After 10 weeks, Susan will have $295 and CiCi will have $259.
Suppose that y varies directly as the square root of X, and that y = 45 when x = 225. What is y when x = 127 Round your answer to two decimal places if
necessary
Answers
Answer:
y=381
Step-by-step explanation:
given: y=45 x=225
y=kx
45=k√(225)
45=k(15)
45=15k
45/15=15k/15
3=k
given: x=127 k=3
y=kx
y=3(127)
y=381
HELPP QUICK PLEASE please
Answers
Hi! I hope you're enjoying your day!
Please remember that an arithmetic sequence is a sequence where we use either addition or subtraction to get to the next term.
Now, let's find an arithmetic sequence here.
Is it Option A?
Remember: It should have a common difference of 2.
Which means we either add or subtract 2 to get to the next term.
Well, it seems like Option A is right.
Let's check the other options.
Is Option B right? Nope.
Here's why.
Hint: Pay attention to the signs.
We have
1, -3, 5, -7, 9...
So Option B is wrong.
Option C is correct, because we subtract 2 each time.
Option D is wrong, because we multiply by 2 each time.
Hence, the right options are
[tex]\boxed{\boxed{\bold{Options~A~and~C.}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{200}{2}[/tex]
Type the correct answer in the box
The value of the expression 23+32-3x4-52 divided by 5+(7x4) is
Answers
Answer:
50.2
Step-by-step explanation:
First we would do parenthesis and then exponents which they aren't
7 x 4=28
then we would do 3 x 4=12
52 divided by 5=10.4
23 + 32=55 - our 3 x 4
55 - 12=43
so 43 - 10.4=32.6-52 divided by 5
32.6 - 10.4 =22.2
And our last step what is 22.2 + 28=50.2
Hope this helps have a great day:)
Which of the following represents an exponential function? Select all that apply
Answers
Answer:
Option B and C are correct.
Step-by-step explanation:
The two graphs in the second picture are the graphs of exponential functions. You can detect it from the L shaped graphs.
The very first graph represents a linear function. A straight line always represents a linear function. In a Linear function, the change in the values of y is constant throughout in relative to change in x values.
The final graph represents a quadratic function rising on both ends.
Answer:
2 and 3 by my knowledge
Step-by-step explanation:
Can someone please help me out?
Answers
Answer:
Step-by-step explanation:
Angie's neighbor sells T-shirts. T-shirts usually cost $20.00. This week,
each shirt is on sale for 20% off, plus 13% tax.
Calculate the sale price of one T-shirt with tax.
Answers
Answer:
$18.08
Step-by-step explanation:
20% off = 20 x 0.8 = 16
plus tax = 16 x 1.13 = 18.08
Answer:
$18.08
Step-by-step explanation:
20% of $20.00 = 0.2 x 20 = $4
Therefore, the sale price of the t-shirt with 20% off = 20 - 4 = $16
If a sales tax of 13% is then applied, final sale price = 16 x 1.13 = $18.08
How can you calculate the area of the circle if know the circle’s circumference.
Answers
Answer:
dont cheat
Step-by-step explanation:
Z is the centroid of UVW
Z is the intersection of the triangle's ______
A. Medians
B. altitudes
C. angle bisectors
D. perpendicular bisectors
Answers
Answer: A
Step-by-step explanation:
The intersection point of the medians of a triangle is defined to be the centroid.
The solution is Option A.
The centroid of the triangle UVW is the intersection of the medians of the triangles
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as UVW
Now , the median of the triangle from U is given by
The measure of WY = The measure of YV
The median of the triangle from W is given by
The measure of UX = The measure of XV
And , the point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians
So , median is a line that joins the midpoint of a side and the opposite vertex of the triangle
Hence , the point Z is the intersection of the triangle's medians
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You move up 5 units and down 3 units. You end at (2, 0). Where did you start?
Answers
Answer:
(0,0)
Step-by-step explanation:
Do the opposite. (2-5+3,0) is (0,0)
Simplify the expression to a polynomial in standard form: (4x-3)(3x^2-2x+1)
Somebody please help
Answers
Answer:
[tex] {12x}^{3} - 17x^{2} + 10x - 3[/tex]
Brainliest if correct
Answers
Answer:
12 divided by 3 is 4
so multiply 1 by 4 and you get... 4
so now its 1/12+4/12 and that comes out to 5/12
Step-by-step explanation:
hope this helps :D
Does this represent a linear relationship or
exponential relationship?
Input Output
3 5
4 7
5 9
6 11
Answers
Answer:
It represents a linear relationship
Step-by-step explanation:
Linear relationship:
- constant change in x and y
Exponential relationship:
- constant change in x
- constant ratio of y
We see that 3, 4, 5, and 6 are a constant change in x as it's going up by +1.
It also has a constant change of y +2.